Good news and maybe some bad news -
That Organic-ville ketchup definitely meets the fat requirement - 20 calories per serving and none from fat. The ingredients have no oils or other hidden sources of fat.
Things of concern -
Calories per serving = 20 Sodium in milligrams should be around 20 - instead it is 125. Jeff allows some wiggle room for condiments, but that is a concentrated dose of salt - about six times the recommended max. The second ingredient on the list is a processed sugar (agave nectar) which is not what you want for weight loss, but a person who doesn't need to lose weight should not worry about small amounts.
Ketchup is easy to abuse for some people. The serving size is 1 Tbsp. I see people use much more than that. The worst thing about it is that it is not a whole plant food. If you want tomato flavor, use a real tomato, or better several.
Let's face it. It is the salt and sugar in this product that makes it popular - not its health benefits. If you are looking for results, you can learn to do without the added salt and sugar.
If you add a good amount of this ketchup to bread (a high calorie density food that is one of my vices and quickly puts weight on me), you are really handicapping your weight loss. The more you can eat plain unrefined whole plant food (which you can get used to and like if you try), the better off you will be IMO. My belief and experience is that there is no magic food that will help weight loss, but that the trick is in re-educating your tastes so that whole plant food is palatable. The taste of the food is in your neuro system, and not in the food itself. You can change your neuro system to like healthy food. You are never going to make especially appealing high calorie density foods and high salt foods healthy. The best foods don't need a label because they are whole plant foods.
I don't know if Jeff would recommend this product. Probably not due to the salt and sugar, but I'm sure he would allow it in small amounts since he is mostly concerned about where the great majority of the calories come from. If the ketchup and bread were a frequent part of the diet, I don't think he would recommend it, especially for somebody trying to lose weight.